1) A plumber and his apprentice took a job at a house with water leaking into th
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Question
1) A plumber and his apprentice took a job at a house with water leaking into the basement from the 1st-floor shower. The plumber suspects that the leak is caused by water from the shower leaking through a loose faucet in the tub below the shower. To test this suspicion, he decides to pour water on the base of the tub faucet. If the faucet is loose, then the water he pours should leak through to the basement.
A) Briefly define each term in the Bayes theorem equation – p(H), p(~H), p(D|H), p(D|~H), p(H|D), and p(~H|D).
B) In one sentence, what is the hypothesis in the plumber example?
C) In one sentence, what is the data in the plumber example?
D) Before the water-pouring test, the apprentice asks the plumber whether a loose faucet is commonly the cause of leaks like this one. The plumber says that a loose faucet is the problem in about 60% of cases like this. State which term in Bayes theorem this information corresponds to, and give a 1-3 sentence explanation of why you picked that term.
E) The plumber directs his apprentice to conduct the water pouring test, and the apprentice reaches to get water from the shower. The plumber stops him and explains that if they get the water from the shower, then they are likely to see a leak even if a loose faucet isn’t the problem. For example, the pipes leading to the shower might be rusty, and this could cause a leak. He directs the apprentice to get the water from the kitchen and pour this water over the tub faucet. With this method, they shouldn’t see any water leak into the basement if the faucet isn’t loose. State which term in Bayes theorem the plumber is affecting by getting the water from the kitchen instead of the shower, and give a 1-3 sentence explanation of why you picked that term.
F) The apprentice gets water from the kitchen to pour over the tub faucet. The plumber notices that the apprentice filled a small cup and sends him back to fill a larger bucket. He explains that the small cup might not have enough water for them to see a leak even if the faucet is loose, but they are very likely to see a leak if they use a whole bucket of water and the faucet is loose. State which term in Bayes theorem the plumber is affecting by using a bucket instead of a small cup, and give a 1-3 sentence explanation of why you picked that term.
2) A) Briefly (1-3 sentences) explain what a p value is.
B) If researchers conduct a significance test with alpha = .05 and get a p value of .03, is the test significant or nonsignificant?
C) If researchers conduct a significance test with alpha = .01 and get a p value of .03, is the test significant or nonsignificant?
Explanation / Answer
2) a) probability value or p value
When we are performing a hypothesis test then the p value determines the significance of our results.
Probability value is always lies between 0 and 1
B) p value = 0.03 < 0.05 then the result is significant and we reject the null hypothesis.
C) p value = 0.03 > 0.01 , then the result is not significant and we don't reject the null hypothesis.
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